The question concerns the state parliament.
The Landtag passes state laws, scrutinises the state government and elects the Minister President. Voters determine its composition through the state election. Five years is the ordinary length of a parliamentary electoral term.
The constitution defines the transition more precisely: the ordinary new election takes place between the 57th and 61st months after the term begins. The current term ends when the new Landtag first meets. It therefore does not end merely when votes are counted on election night.
The other three answers
A political crisis does not make another number the ordinary rule.
3
Three years is not the duration set by Article 50. An actually shorter interval would need a special explanation.
4
Four years is not the Thüringen Landtag’s current ordinary term. Do not transfer figures from other parliaments without checking.
6
Six years exceeds the ordinary five-year term.
Early elections require constitutional conditions.
Under Article 50’s conditions, the Landtag can resolve to dissolve itself with two thirds of its members. There is also a route after a failed confidence vote if no new Minister President is elected within three weeks.
A change of Minister President is not automatically a new state election. The constitution treats appointment of the government and election of parliament separately.
Article 50 · Constitution of Thüringen ↗Thüringen Landtag → normally five years.
Keep the ordinary duration separate from a possible early election.
Three words for this question
- die Wahlperiodeelectoral term
- The constitutional term of an elected parliament.
- die Auflösungdissolution
- Bringing a parliament to an early end under the applicable rules.
- die Vertrauensfrageconfidence vote
- A procedure through which the head of government tests parliamentary support.